Ever since the epic work of Yvonne Choquet-Bruhat on the well-posedness of Einstein's equations initiated the mathematical study of general relativity, women have played an important role in many areas of mathematical relativity. In this workshop, some of the leading women researchers in mathematical relativity present their work.

A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available.

A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.

MSRI has a preferred rate of $149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. There is no cut-off date for reservations. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and enter dates of stay at top of screen and click Book Now. Once on the reservation page, click "Preferred/Corporate Rate Accounts" and input the code: msri.

To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show the MSRI rate on all room types available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.

MSRI has preferred rates of $149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri.

Since the time of Gauss, geometers have been interested in the interplay between the intrinsic structure of hypersurfaces and their extrinsic geometry from the ambient space. Many classical results discuss the sectional curvature. For example, it is known that a complete hypersurface in Euclidean space with non-negative sectional curvature is either convex or a generalized hypercylinder.
In a series of joint work with Damin Wu, we study hypersurfaces with non-negative scalar curvature. We prove that a closed hypersurface with nonnegative scalar curvature must be weakly mean convex. In general, vanishing scalar curvature causes analytical difficulties because the scalar curvature operator may not be elliptic. We tackle the problem by studying the level sets of a height function, which is motivated by general relativity. We further extend our proof to unbounded hypersurfaces which are asymptotically flat at infinity and obtain applications in the positive mass theorem and the Penrose inequality.

Riemannian 3-manifolds with prescribed scalar curvature arise naturally in general relativity as spacelike hypersurfaces in the underlying spacetime. In 1993, Bartnik introduced a quasi-spherical construction of metrics of prescribed scalar curvature on 3-manifolds. This quasi-spherical ansatz has a background foliation with round metrics and converts the problem into a semi-linear parabolic equation. It is also known by work of R. Hamilton and B. Chow that the evolution under the Ricci flow of an arbitrary initial metric $g_0$ on $S^2$, suitably normalized, exists for all time and converges to the round metric.
In this talk, we describe a construction of metrics of prescribed scalar curvature using solutions to the Ricci flow. Considering background foliations given by Ricci flow solutions, we obtain a parabolic equation similar to Bartnik’s. We discuss conditions on the scalar curvature that guarantees the solvability of the parabolic equation, and thus the existence of asymptotically flat 3-metrics with a prescribed inner boundary. In particular, many examples of asymptotically flat 3-metrics with outermost minimal surfaces are obtained

We provide a framework for analyzing axially symmetric harmonic maps on R3 with symmetric
target spaces G=K. Drawing on results from analysis to Lie theory to geometry, we give a complete
and rigorous proof that, all such maps are completely integrable. We further demonstrate that
new solutions to the harmonic map equations can be generated from a given seed solution, using a
dressing or vesture method. This unies the integrability of theories including chiral eld models,
nonlinear -models, Yang-Mills and Einstein electrovacuum equations in the general context of
harmonic maps.
Utility of the vesture method is made concrete by generating N-solitonic harmonic maps into a
noncompact Grassmann manifold G = SU(p; q). We demonstrate a special case by deriving Kerr
and Kerr-Newman solutions from the Minkowski initial seed for the Einstein vacuum and Einstein-
Maxwell cases, respectively. In performing an asymptotic analysis, these solutions are shown to be
in the hyperextreme sector of the corresponding parameters, suggesting constraints on the dressing
mechanism. We indicate the possibility of using this analysis to control the resulting N-black hole
configurations in this setting.

Einstein's theory of General Relativity predicts a Cosmos with black holes and gravitational waves.
Although neither black holes nor gravitational waves have been directly detected, their presence is
already felt throughout the Universe. This decade will witness observations for which gravitational
waves are the messengers that deliver information in exquisite detail about astrophysical phenomena,
among them the collision of two black holes, a system completely invisible to the eyes of traditional
telescopes. Models that predict gravitational wave signals from likely sources are crucial
for the success of this endeavor. Modeling sources of gravitational radiation requires solving the
Eintein equations of General Relativity using powerful computer hardware and sophisticated
numerical algorithms. In this talk I will review these challenges, how we have overcome them, and
what we have learned along the way. Our predictions of the gravitational waves from the black holes
collisions is one pivotal step in ushering in the new era of gravitational-wave astronomy.

Electromagnetic emissions from gravitational wave sources such as supermassive black hole binaries will carry additional information of the environment in which the source is embedded. Using techniques from numerical relativity, the coupled Einstein equations with matter fields let us study the dynamical spacetimes of non-vacuum binary mergers in fully non-linear general relativity with matter probing the most dynamic strong regime of the system. We discuss the current understanding of anticipated electromagnetic counterparts from astrophysical environments probing the highly dynamic spacetime surrounding these strong gravitational wave sources.

We will review the notion of mass for asymptotically hyperbolic manifolds, and discuss the respective positive mass conjecture and Penrose conjecture. We will also address the nearly equality case of the positive mass theorem: if the mass is small, can we say that the metric is close to the hyperbolic metric in some sense? A part of the new results to be presented comes from joint work with Mattias Dahl and Romain Gicquaud.

We introduce new geometric evolution equations for hypersurfaces in asymptotically flat Riemannian manifolds, and discuss a natural application of these null mean curvature flows to locating marginally outer trapped surfaces (MOTS) - which play the role of quasi-local black hole boundaries in general relativity